Atmospheric neutrinos as a probe of eV^2-scale active-sterile oscillations
aa r X i v : . [ h e p - ph ] J u l Atmospheric Neutrinos as a Probe of eV -scaleActive-Sterile Oscillations Raj Gandhi a ) , and Pomita Ghoshal a ) 2 a ) Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad - 211019, India.
Abstract
The down-going atmospheric ν µ and ¯ ν µ fluxes can be significantly altered due to the presence ofeV -scale active-sterile oscillations. We study the sensitivity of a large Liquid Argon detector and alarge magnetized iron detector (like the proposed ICAL at INO) to these oscillations. Such oscilla-tions are indicated by results from LSND, and more recently, from MiniBooNE and from reanalysesof reactor experiments following recent recalculations of reactor fluxes. There are other tentative in-dications of the presence of sterile states in both the ν and ¯ ν sectors as well. Using the allowed sterileparameter ranges in a 3+1 mixing framework in order to test these results, we perform a fit assumingactive-sterile oscillations in both the muon neutrino and antineutrino sectors, and compute oscillationexclusion limits using atmospheric down-going muon neutrino and anti-neutrino events. We find that(for both ν µ and ¯ ν µ ) a Liquid Argon detector, an ICAL-like detector or a combined analysis of bothdetectors with an exposure of 1 Mt yr provides significant sensitivity to regions of parameter space inthe range 0 . < ∆ m < for sin µµ ≥ .
08. Thus atmospheric neutrino experiments can pro-vide complementary coverage in these regions, improving sensitivity limits in combination with boundsfrom other experiments on these parameters. We also analyse the bounds using muon antineutrinoevents only and compare them with the results from MiniBooNE.
Some significant recent experimental results in neutrino physics (MiniBooNE [1], reactor ¯ ν e flux recal-culation [2, 3], gallium data [4], CMB and big bang nucleosynthesis data [5, 6, 7]), along with the olderLSND [8] result, have provided evidence of ¯ ν µ → ¯ ν e oscillations at values of L/E ≈ L is the baseline and E the neutrino energy. This has motivated the addition of one or more sterileanti-neutrino(s) with eV-scale mass(es) to the standard 3-flavour scenario. While the experimentalevidence remains intriguing, no clearly preferred theoretical model or framework has emerged so far.These results have prompted a number of global analyses incorporating recent data as well asresults from earlier experiments, which assume either a framework of three light active neutrinos andone (”3+1”), or two (”3+2”) sterile neutrinos [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,24, 25, 26, 27].Efforts to clarify the situation include plans to put in a new near detector or re-using the existingMiniBooNE detector at a near baseline[28]. There is also a proposal to use the ICARUS detector, aLiquid Argon time projection chamber at the CERN-PS to look for sterile neutrinos[29]. It has alsobeen suggested that a large future liquid scintillator detector like NO ν A or LENA be coupled witha compact decay-at-rest source at a short baseline in order to confirm or refute the signals of sterileneutrinos[30].In this situation, it is useful to look at experiments which can provide data at multiple values of L and E , which would unambiguously signal the presence, or absence, of oscillations. It is also desirableto move to a class of experiment with backgrounds and uncertainties which are qualitatively differentfrom those encountered in, for instance, MiniBooNE and LSND, or in reactors. [email protected] [email protected] otivated by these considerations, in this paper we study the role a large atmospheric detectorcan play in clarifying these issues. Two examples of such upcoming detectors are the proposed ICALat INO [31] and a large Liquid Argon detector [32, 33, 34]. For simplicity, we consider the down-going muon neutrino and muon anti-neutrino events in the energy range 1 −
20 GeV and baselinerange 10 −
100 km. This provides a wide band of
L/E with values that are relevant to the issuesat hand. The lepton charge identification capability of such detectors, if magnetized, lends an edgeby allowing discrimination between the neutrinos and anti-neutrinos, compared to a water Cerenkovdetector like SuperKamiokande. It allows independent tests of the presence of sterile neutrinos in themuon and anti-muon data samples, with higher statistical significance for the former due to the larger(by approximately a factor of two) neutrino-nucleon charged current cross section .In the parameter range under study, strong sterile parameter constraints already exist from CDHS[35], CCFR [36], MINOS[37, 38, 18], SciBooNE/MiniBooNE [39] and SuperKamiokande atmosphericneutrino data [9, 40, 41]. The present limits are summarized in [16]. Recently, even stronger boundsfrom MINOS+ have been suggested in [42], and the possibility of sterile neutrino information fromatmospheric neutrino data in IceCube has been discussed in [43]. Less stringent constraints also existfor the ¯ ν µ sector from MiniBooNe[44, 45].In Section 2, we motivate our study of sterile-scale oscillations using downgoing atmospheric muonneutrinos, and give the specifications of the two futuristic detectors we have analysed for this purpose.Section 3.1 gives our results for the exclusion limits from these detectors in the sin µµ − ∆ m plane,comparing them with bounds obtained from the experiments listed above.Since both LSND and MiniBooNE have provided evidence of eV oscillations in the ¯ ν µ sector, weseparately investigate in Section 3.2 the expected signal from ¯ ν µ → ν x , utilizing the charge identi-fication capability of such detectors, for a comparison with the bounds from MiniBooNE. Section 4summarizes our results and conclusions. Muon and electron neutrinos and anti-neutrinos produced in the earth’s atmosphere provide a natu-rally occurring source of large fluxes spanning an extensive range of energies and baselines. While theupward-going electron and muon neutrinos with baselines of several thousands of Kms pass throughthe earth, are influenced by earth matter effects and give good sensitivity to standard 3-flavour neu-trino oscillation parameters, the downward-going neutrinos have baselines of about 15 - 130 Kms.With an energy range between 1-20 GeV (above which fluxes become small), these neutrinos lie in theL/E range in which oscillations arising from the sterile mass-squared difference may be observed.Assuming a 3+1 scheme (one non-standard neutrino with a mass squared difference of ∆ m (=∆ m ) ∼ ), the expressions for the relevant survival and oscillation probabilities with 2-flavoursterile-scale oscillations are [14]: P µµ = 1 − sin µµ sin [∆ m L/ E ] P eµ = sin eµ sin [∆ m L/ E ] It is not our intention here to assume that there is CPT violation, i.e. that ν and ¯ ν oscillate differently. Our resultsbelow are based on a combined analysis of ν + ¯ ν events. Since the detectors in question can identify lepton charge effectively,we also provide results for ¯ ν alone, for comparison with MiniBooNE and LSND, which see a signal predominantly in ¯ ν . here Θ µµ and Θ eµ are given by sin µµ = 4 | U µ | (1 − | U µ | ), sin eµ = 4 | U e | | U µ | , and U is the 4 × σ ranges of these parameters:sin bfµµ = 0 . , . ≤ sin µµ ≤ .
25 (1)sin bfeµ = 0 . , × − ≤ sin eµ ≤ . m ) bf = 0 . , . ≤ ∆ m ≤ Here the superscript bf denotes the best-fit values.We perform our statistical analysis using two kinds of proposed detectors: • A large Liquid Argon detector, which can detect charged particles with very good resolutionover the energy range of MeV to multi GeV, with magnetization over a 100 kT volume with amagnetic field of about 1 Tesla [46]. We assume the following energy resolutions over the rangesrelevant to our calculations [33]: σ E e = 0 . , σ E µ = 0 . σ E had = q (0 . /E had + (0 . σ θ e = 0 .
03 radians = 1 . o , σ θ µ = 0 .
04 radians = 2 . o σ θ had = 0 .
04 radians = 2 . o (2)where E e , E µ and E had are the lepton and hadron energies in GeV, σ E are the energy resolutionsand σ θ are the angular resolutions of electrons, muons and hadrons as indicated. The energy res-olution in terms of the neutrino energy is related to the leptonic and hadronic energy resolutionsas follows: σ ν /E ν = q (1 − y ) ( σ lep /E lep ) + y ( σ had /E had ) (3)Here the rapidity or the Bjorken scaling variable y is defined as y = E had /E ν , where E ν = E lep + E had is the energy of the neutrino. The relation E ν = E lep + E had is exact for quasi-elastic scattering and the closest analytic approximation for DIS scattering. Lepton-neutrinocollinearity is assumed in this procedure, and is expected to hold true to a good approximationin the multi-GeV neutrino energy range. Hence the energy resolution in terms of the neutrinoenergy is given by σ E ν = q (0 . + (0 . /yE ν + (0 . (4)for both electron and muon neutrinos. In our computation, we take the average rapidity in theGeV energy region to be 0.45 for neutrinos and 0.3 for antineutrinos [47]. These average rapidityvalues have been verified to be accurate using realistic hadron event simulations. The angularresolution of the detector for neutrinos can be worked out to be σ θ νe = 2 . o , σ θ νµ = 3 . o . Theenergy threshold and ranges in which charge identification is feasible are E threshold = 800 MeVfor muons and E electron = 1 − • An iron calorimeter detector like ICAL, which, like the above detector, offers the advantage ofmuon charge discrimination using magnetization with a field of 1.3 Tesla, allowing a separateobservation of atmospheric muon neutrino and anti-neutrino events. For this detector, standardresolutions of 10 o in angle and 15% in energy are assumed.
10 15 20 E ν N µ+µ no sterile oscillationsin Θ µµ = 0.083, ∆ m = 0.9 eV LAr (1 Mt yr) down µ + µ CC events, cos θ z = 0.25 to 0.3 E ν N µ+µ no sterile oscillationsin Θ µµ = 0.083, ∆ m = 0.9 eV LAr (1 Mt yr) down µ + µ CC events, cos θ z = 0.45 to 0.5 Figure 1:
LAr downgoing µ + ¯ µ event spectrum vs neutrino energy integrated over the 2 specific cos θ z bins with andwithout 2-flavour sterile-scale oscillations, using best-fit sterile parameter values. The muon event rates are a function of both P µµ and P eµ , but P eµ is highly suppressed due to thesmallness of the parameter sin eµ . Thus the downgoing muon event spectrum reflects the behaviourof P µµ and shows signatures of the sterile parameters Θ µµ and ∆ m . In Figure 1, the downgoing muonneutrino distribution with and without two-flavour sterile oscillations is shown as a function of theneutrino energies, integrated over cos θ z bins.We assume a 1 Mt yr exposure for both types of detectors, standard detector resolutions asabove, and flux uncertainties and systematic errors incorporated by the pull method [48]. The valuesof uncertainties are chosen as in [49]: flux normalization error 20%, flux tilt factor, zenith angledependence uncertainty 5%, overall cross-section uncertainty 10%, overall systematic uncertainty 5%.We take a double binning in neutrino energy and zenith angle in the energy range 1-20 GeV and cos θ z range 0.1 to 1.0. To be consistent with the detector resolution, the bin widths are required to be ≥ the resolution widths. For the above neutrino energy and zenith angle ranges, this allows us to take20 energy bins and 18 angle bins for these values of resolution width. The atmospheric fluxes aretaken from the 3-dimensional calculation in [50]. We have taken into account the neutrino productionheight distribution in the atmosphere [51]. ν µ and ¯ ν µ event spectra One can extract the statistical sensitivity with which experimental-set ups like the ones describedabove may be able to constrain sterile parameters using the downgoing muon and anti-muon eventspectra as the signal. We perform this study in two stages:a) The best exclusion limits possible from this analysis are determined using simultaneously thedowngoing ν µ and ¯ ν µ event spectra for both kinds of detectors and doing a combined fit.b) In order to test the MiniBooNE/LSND antineutrino results, the atmospheric downgoing ¯ ν µ event spectra with sterile oscillations for both kinds of detectors are analysed to determine the sterileparameter bounds, and compared with the bounds from MiniBooNE. ν µ , ¯ ν µ analysis For this study, the sterile oscillation exclusion limits are computed by combining both the atmosphericdowngoing muon and antimuon event spectra with sterile-scale oscillations. This involves taking i) ∆ m [ e V ] sin Θ µµ Exclusion contours in the sin Θ µµ - ∆ m plane with ν µ , anti- ν µ events Lar, 1 Mt yr
Lar 3 σ Lar 90%Sci/MB 90%MINOS 90%CDHSW 99%atm 99% ∆ m [ e V ] sin Θ µµ Exclusion contours in the sin Θ µµ - ∆ m plane with ν µ , anti- ν µ events ICAL, 1 Mt yr
ICAL 3 σ ICAL 90%Sci/MB 90%MINOS 90%CDHSW 99%atm 99% (a) (b)
Figure 2:
Exclusion curves using (a) Liquid Argon and (b) ICAL downgoing muon and anti-muon events with sterileoscillations - Comparison with 99% c.l. limit from atmospheric analysis [16, 9], 90% limits from SciBooNE/MiniBooNE [39]and MINOS [37], 99% c.l. limit from CDHSW [16, 35]. the ’expected’ spectrum N th , in which sterile oscillations are included, and ii) the ’observed’ spectrum N ex (no − osc), where ’no-osc’ indicates no sterile-scale oscillations. Since we expect no differencesin the oscillations of neutrinos compared to antineutrinos in the 3+1 model when matter effects areabsent, we have assumed equal probabilities for them for downgoing events. The exclusion limits arepresented in Figure 2 for a Liquid Argon detector and an ICAL detector, with an exposure of 1 Mtyr for both. Figure 3 shows the results from a combined analysis of ICAL + Liquid Argon. Thebounds obtained from our analysis are compared with the 99% c.l. exclusion region from atmosphericneutrino data [16, 9], the 90% limits from SciBooNE/MiniBooNE [39] and MINOS [37] and the 99%limit from the CDHSW disappearance analysis [16, 35].With a Liquid Argon detector and an exposure of 1 Mt yr, regions greater than sin µµ ∼ .
09 can be excluded at 90% c.l. with a combination of muon and anti-muon events over mostof the allowed ∆ m range. An ICAL-like detector with a similar exposure gives a weaker 90% c.l.exclusion bound at sin µµ ∼ .
15. A combined analysis of the two experiments gives a 3 σ exclusionbound for sin µµ ≥ .
11, and a 90% c.l. limit for sin µµ ≥ .
08, which is seen to be animprovement over the earlier bounds obtained from atmospheric neutrinos, as well as those fromCDHSW, SciBooNE/MiniBooNE and MINOS, over significant regions of the parameter space. Notethat the sensitivity using this set-up is better in the low ∆ m region (∆ m < ), part of which liesoutside the present global fit range, but our purpose here is to demonstrate that such an experimentis capable of providing significant bounds over the entire parameter space which can contribute toconstraining sterile parameters in combination with other experiments in a future global analysis. ¯ ν sector Here we compute the sterile oscillation exclusion limits using the downgoing antimuon event spectrumfor comparison with the results from MiniBooNE/LSND antineutrino data. The bounds obtained fromthis analysis are presented in Figure 4. The left and right panels correspond to the exclusion boundsfor the parameters ¯∆ m and sin µµ with the downgoing ¯ ν µ spectrum for an ICAL detector and aLiquid Argon detector respectively, both with an exposure of 1 Mt yr. Here ¯∆ m and Θ µµ denote themixing parameters for antineutrinos. The 90% exclusion limit from MiniBooNE [45] is superimposed ∆ m [ e V ] sin Θ µµ Exclusion contours in the sin Θ µµ - ∆ m plane with ν µ , anti- ν µ events ICAL + Lar (1 Mt yr)
ICAL+Lar 3 σ ICAL+Lar 90%Sci/MB 90%MINOS 90%CDHSW 99%atm 99%
Figure 3:
Same as Figure 2 using ICAL + Liquid Argon downgoing muon and antimuon events. ∆ m [ e V ] sin Θ µµ Exclusion contours in the sin Θ µµ - ∆ m plane with anti- ν µ events ICAL, 1 Mt yr
ICAL 3 σ ICAL 90%MiniBooNE 90% ∆ m [ e V ] sin Θ µµ Exclusion contours in the sin Θ µµ - ∆ m plane with anti- ν µ events Lar, 1 Mt yr
Lar 3 σ Lar 90%MiniBooNE 90% (a) (b)
Figure 4:
Exclusion curves using (a) ICAL and (b) Liquid Argon downgoing anti-muon events with sterile oscillations -Comparison with 90% exclusion limit from MiniBooNE [45] antineutrino analysis. on both figures. It can be seen that this set-up provides a 90% c.l. exclusion capacity with an ICAL-like detector with an exposure of 1 Mt yr for about sin µµ > . . < ¯∆ m < , and for a Liquid Argon detector with an exposure of 1 Mt yr for about sin µµ > .
15 for arange 0 . < ¯∆ m < . Thus a Liquid Argon detector gives stronger bounds than those from theMiniBooNE antineutrino analysis. In this paper, we have studied the possible sensitivity of atmospheric neutrino data in a large mag-netized iron calorimeter detector like the proposed ICAL at INO and a large Liquid Argon detector,to eV -scale active-sterile oscillations. Such detectors are capable of distinguishing lepton charge andhence discriminating between neutrino and antineutrino events. With the present sterile parameterranges in a 3+1 mixing framework, down-going atmospheric ν µ and ¯ ν µ events can show signaturesof eV -scale oscillations, due to their suitable energy and baseline range (neutrinos with multi-GeVenergies and baselines ranging from about 10 to 100 Kms). Our analysis has been done in two parts: To be consistent with homogeneity in ν − ¯ ν behaviour in the 3+1 scenario, we assumed identicalactive-sterile oscillations in both the muon neutrino and antineutrino sectors and derived active-sterile oscillation exclusion limits (Figures 2 and 3), comparing them with the limits obtainedfrom [39, 37, 16, 17, 35, 9].a) With a Liquid Argon detector (1 Mt yr), regions greater than sin µµ ∼ .
09 can be excludedat 90% c.l. with a combination of muon and anti-muon events, over most of the ∆ m range. A3 σ exclusion bound is possible for sin µµ ∼ . µµ ∼ .
15 with a combination of muon and anti-muon events.c) With a combined analysis of ICAL (1 Mt yr) and Liquid Argon (1 Mt yr), a 90% c.l. exclusionlimit is obtained for sin µµ ≥ .
08 and a 3 σ bound for sin µµ ≥ .
11, which comparesfavorably with present limits from CDHSW, MINOS, MiniBooNE and atmospheric neutrinos. • For testing the predictions of LSND and MiniBooNE, we performed a fit with active-sterileoscillations in the muon antineutrino sector, comparing the results with the exclusion limitsfrom MiniBooNE (Figure 4), and derived the following 90% c.l. exclusion bounds:a) an ICAL-like detector with an exposure of 1 Mt yr for about sin µµ > . . < ¯∆ m < ,b) A Liquid Argon detector with an exposure of 1 Mt yr for about sin µµ > .
15 for a range0 . < ¯∆ m < .The limits for both detectors from an exposure of 1 Mt yr may be accessible in a time-frame ofabout 10-15 years.In conclusion, a down-going event analysis using large future atmospheric detectors may be helpfulin providing significant complementary constraints on the sterile parameters, which can strengthenexisting bounds when combined with other experimental signatures of sterile-scale oscillations. Sucha set-up exhibits better sterile oscillation sensitivity in the low ∆ m region (∆ m < ). Evidence(or the lack of it) from such detectors has the advantage of originating in a sector which is differentfrom those currently providing clues pointing to the existence of sterile neutrinos (i.e short-baselineexperiments). Additionally, it permits access to a wide-band of L/E , which is important if oscillatorybehaviour is to be unambiguously tested.
We acknowledge long-standing collaborations on INO/ICAL physics with Srubabati Goswami and S.Uma Sankar, which have informed this work. RG would like to acknowledge the hospitality of theCern Theory Division, where this work was initiated. He is also grateful for financial support fromthe DAE XI Plan Neutrino project. PG thanks S.T. Petcov for useful discussions. This work wassupported in part by the INFN program on ”Astroparticle Physics” (PG).
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